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On the Existence of Smooth Lyapunov Functions for Arbitrary Closed Sets

On the Existence of Smooth Lyapunov Functions for Arbitrary Closed Sets We give a simpler proof of the existence of isolating blocks due to Conley and Easton (Trans Am Math Soc 158:35–61, 1983) based on a generalization of the work of Wilson Jr. and Yorke (J Differ Equ 13:106–123, 1973) on Lyapunov functions and isolating blocks. This will also yield a proof of Massera’s (Ann Math 64:182–206, 1956) converse Lyapunov Theorem and a proof of a Theorem independently due to Duistermaat and Hörmander (Acta Math 128:183–269, 1972) and Sullivan (Invent Math 36:225–255, 1976). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Bulletin of the Brazilian Mathematical Society, New Series" Springer Journals

On the Existence of Smooth Lyapunov Functions for Arbitrary Closed Sets

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References (23)

Publisher
Springer Journals
Copyright
Copyright © Sociedade Brasileira de Matemática 2022
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-022-00291-y
Publisher site
See Article on Publisher Site

Abstract

We give a simpler proof of the existence of isolating blocks due to Conley and Easton (Trans Am Math Soc 158:35–61, 1983) based on a generalization of the work of Wilson Jr. and Yorke (J Differ Equ 13:106–123, 1973) on Lyapunov functions and isolating blocks. This will also yield a proof of Massera’s (Ann Math 64:182–206, 1956) converse Lyapunov Theorem and a proof of a Theorem independently due to Duistermaat and Hörmander (Acta Math 128:183–269, 1972) and Sullivan (Invent Math 36:225–255, 1976).

Journal

"Bulletin of the Brazilian Mathematical Society, New Series"Springer Journals

Published: Sep 1, 2022

Keywords: Flow; Smooth Lyapunov; Converse Lyapunov; Isolating block

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